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- [/============================================================================
- Boost.odeint
- Copyright 2011-2012 Karsten Ahnert
- Copyright 2011 Mario Mulansky
- Copyright 2012 Sylwester Arabas
- Use, modification and distribution is subject to the Boost Software License,
- Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
- http://www.boost.org/LICENSE_1_0.txt)
- =============================================================================/]
- [section Stepper]
- This concepts specifies the interface a simple stepper has to fulfill to be used within the __integrate_functions.
- [heading Description]
- The basic stepper concept.
- A basic stepper following this Stepper concept is able to perform a single step of the solution /x(t)/ of an ODE to obtain /x(t+dt)/ using a given step size /dt/.
- Basic steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers.
- Depending on the actual stepper, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system.
- Note that all error steppers are also basic steppers.
- [heading Refinement of]
- * DefaultConstructable
- * CopyConstructable
- [heading Associated types]
- * '''<para>'''[*state_type]'''</para>'''
- '''<para>'''`Stepper::state_type`'''</para>'''
- '''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>'''
- * '''<para>'''[*deriv_type]'''</para>'''
- '''<para>'''`Stepper::deriv_type`'''</para>'''
- '''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>'''
- * '''<para>'''[*time_type]'''</para>'''
- '''<para>'''`Stepper::time_type`'''</para>'''
- '''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>'''
- * '''<para>'''[*value_type]'''</para>'''
- '''<para>'''`Stepper::value_type`'''</para>'''
- '''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>'''
- * '''<para>'''[*order_type]'''</para>'''
- '''<para>'''`Stepper::order_type`'''</para>'''
- '''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</para>'''
- * '''<para>'''[*stepper_category]'''</para>'''
- '''<para>'''`Stepper::stepper_category`'''</para>'''
- '''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `stepper_tag`.'''</para>'''
- [heading Notation]
- [variablelist
- [[`Stepper`] [A type that is a model of Stepper]]
- [[`State`] [A type representing the state /x/ of the ODE]]
- [[`Time`] [A type representing the time /t/ of the ODE]]
- [[`stepper`] [An object of type `Stepper`]]
- [[`x`] [Object of type `State`]]
- [[`t`, `dt`] [Objects of type `Time`]]
- [[`sys`] [An object defining the ODE. Depending on the Stepper this might be a model of __system, __symplectic_system, __simple_symplectic_system or __implicit_system ]]
- ]
- [heading Valid Expressions]
- [table
- [[Name] [Expression] [Type] [Semantics]]
- [[Get the order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper.]]
- [[Do step] [`stepper.do_step( sys , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in place in `x`.] ]
- [/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in place in `x`.] ]
- [/ [Do step out-of-place] [`stepper.do_step( sys , in , t , out , dt )`] [`void`] [Performs one step. The newly obtained state is written to `out`] ]
- ]
- [heading Models]
- * `runge_kutta4`
- * `euler`
- * `runge_kutta_cash_karp54`
- * `runge_kutta_dopri5`
- * `runge_kutta_fehlberg78`
- * `modified_midpoint`
- * `rosenbrock4`
- [endsect]
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